This article is cited in 4 papers

Brief communications

Local groups and their representations

S. A. Grigoryan^a, A. Yu. Kuznetsova<sup>b

a</sup> Kazan State Energy University, 51, Krasnoselskaya str., Kazan 420066 Russia
^b Kazan Federal Univercity, 18, Kremlevskaya str., Kazan, 420008 Russia

Abstract: In the paper the notion of a local group is applied in the context of operator algebras, and $C^*$-algebraic constructions are proposed related to the local group. For local group we define $*$-representation and strong $*$-representation which are connected by the extension of the local group. Local group allows you to define the regular representation which is a $*$-representation, and the respective reduced $C^*$-algebra, the last is graded over the extension of the local group.

Keywords: Local group, partial isometry, group partial representation, regular representation, graded $C^*$-algebra.

UDC: 517.98

Received: 20.03.2020
Revised: 20.03.2020
Accepted: 25.03.2020

DOI: 10.26907/0021-3446-2020-6-73-78

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:6, 63–68

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